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<h1>direct_method_tfsa
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="box"><strong>GENERATE BILINEAR TIME-FREQUENCY TRANSFORMATIONS USING THE DIRECT METHOD</strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="fragment"><pre class="comment"> GENERATE BILINEAR TIME-FREQUENCY TRANSFORMATIONS USING THE DIRECT METHOD

 BILINEAR TRANSFORMATIONS transform the time domain signal (the
 variable INPUT SIGNAL) to an output time-frequency distribution (the
 variable OUTPUT TIME-FREQUENCY ARRAY)

 These functions use a direct implementation rather than using the
 quadratic time-frequency implementation. This results in a
 computationally optimised routine.
 
 The different types of time-frequency distributions that can be
 implemented directly are:
   
   (i)    Wigner-Ville Distribution 
   (ii)   Short-Time Fourier Transform
   (iii)  Spectrogram
   (iv)   Rihaczek
   (v)    Windowed-Rihaczek

   The various parameters associated with the distributions are as follows:

   TIME-FREQUENCY ARRAY (tfd)

      The computed time-frequency distribution.  size(tfd) will
      return [a, b], where a is the next largest power of two above
      FFT length, and b is floor(length(signal)/time_res) - 1.

   INPUT SIGNAL

      Input one dimensional signal to be analysed. An analytic signal
      is required for this function, however, if signal is real, a
      default analytic transformer routine will be called from this
      function before computing tfd.

   TIME RESOLUTION

      The number of time samples to skip between successive time slices.

   LAG WINDOW LENGTH

      This is the lag window length and controls the size of the
      signal kernel (or instantaneous autocorrelation function) used
      for analysis (lag_window_length must be odd). The kernel used
      will be defined from -(lag_window_length+1)/2 to
      +(lag_window_length+1)/2 in both time and lag dimensions.

   FFT Length:

      Zero-padding at the FFT stage of the analysis may be specified
      by giving an FFT length larger than lag window length.  If
      FFT length is not specified, or is smaller than the
      lag window length, then the next highest power of two above
      lag window length is used.  If FFT length is not a power of
      two, the next highest power of two is used.



  See Also:  <a href="wvd.html" class="code" title="">wvd</a>, <a href="spec.html" class="code" title="">spec</a>, <a href="rihaczek.html" class="code" title="">rihaczek</a>, <a href="analyt.html" class="code" title="">analyt</a></pre></div>

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